When a carrier ps is passed through a ps saturator at temperature T0 containing liquid or solid reagent under conditions leading to its saturation with an equilibrium vapor pressure p-degrees of the reagent, and then into a tube where the exit stream temperature is increased to T(infinity), the downstream partial pressure of reagent, p(infinity), may be less than p-degrees due to thermal diffusion of the reagent driven by the temperature gradient. The mass transfer process has been modeled for two cases : (1) a linear temperature gradient over a tube length L2 and (2) a tube length L1 of constant temperature T0 followed by a tube length L2 with a linear temperature gradient. Solution of case (1) is defined by the dimensionless Peclet number Pe2 = vL2/D and a dimensionless "thermal diffusion number" Td = alphaln(T(infinity)/T0), where v is average ps velocity in the tube, D is the reagent gas-carrier gas binary diffusion coefficient, and alpha is the reagent gas-carrier gas thermal diffusion factor. Solution of case (2) is characterized by Td, Pe2, and Pe1 = vL1/D. Chemical vapor deposition processes used in the fabrication of electronic and optoelectronic semiconductor devices require the reproducible control of reagent partial pressures to better than +/-0.4%. Gas saturators for these processes are commonly operated under conditions where p(infinity) is dependent on both flow rate and the downstream temperature profile, and where p(infinity) can be as much as 10% lower than p-degrees. The reproducible control of reagent partial pressure is best brought about by designing the saturator system so that Pe1 > 10, conditions leading to p(infinity) congruent-to p-degrees independent of flow rate or downstream temperature.